Choose the odd number: 121, 169, and 289 are squares of primes (11^2, 13^2, 17^2). One number is the square of a composite (15^2). Identify that odd square.

Introduction / Context:All four are perfect squares, but three are squares of primes while one is the square of a composite integer, making it the odd one out.

Given Data / Assumptions:

• 121 = 11^2 (prime base).
• 169 = 13^2 (prime base).
• 289 = 17^2 (prime base).
• 225 = 15^2 (composite base; 15 = 3 * 5).

Concept / Approach:Classify by the nature of the base whose square forms the number: prime versus composite.

Step-by-Step Solution:

Verification / Alternative check:Factor 225 = 15 * 15 = (3 * 5) * (3 * 5) = 3^2 * 5^2; the base 15 is not prime.

Why Other Options Are Wrong:121, 169, and 289 are squares of prime bases, matching the majority rule.

Common Pitfalls:Assuming all squares are alike without considering the primality of the base.

Final Answer:225 is the odd square (square of a composite).